A store has a $40\%$ off sale on headphones. With this discount, the price of one pair of headphones is $\$36$. What is the original price of the pair of headphones? $\$$
Answer: The discount is $40\%$, so the discounted cost represents the original price $(100\%)$ minus the discount $(40\%)$. $100\%-40\%=60\%$ The discounted price of $\$36$ is $60\%$ of the original price. To find the original price, first we need to answer, $\${36}$ is ${60}\%$ of what number? Percent means per hundred, so ${60}\%$ is equivalent to ${\dfrac{60}{100}}$ which is also equal to ${60 \div 100}$. ${60 \div 100 = 0.6}$ To find the original price, we need to know ${0.6}$ times what number equals ${36}$. ${0.6} {x} = {\$36}$ $\begin{aligned} {0.6} {x} &= {\$36} \\\\ \dfrac{{0.6} {x}}{{0.6}} &= \dfrac{{\$36}}{{0.6}} \\\\ {x} &= {60} \end{aligned}$ The original price of the pair of headphones is $\${60}$.